ON A SPECIAL CLASS OF FINITE p-GROUPS OF MAXIMAL CLASS - Xue, Haibo; Lv, Heng; Chen, Guiyun (Italian Journal of Pure and Applied Mathematics, 2014)
In this paper, we study the finite p—group G of maximal class in which every nonabelian subgroup H satisfies CG(H) = Z(H). We prove here that a finite p—group G of maximal class is metabelian if every nonabelian subgroup H satisfies CG(H) = Z(H), furthermore, if p ≠ 3, |G| ≥ ¸p2p, then there is an abelian subgroup of index p in G.